Suarez, who served a seven-game suspension for a bite during a Dutch league match in 2010, was foiled by Ivanovic as he attempted to kick the ball between the center back's legs in the penalty area. As the ball rebounded toward the edge of the area, Suarez turned to his opponent, and television images clearly showed him biting into Ivanovic's jersey at the top of the right arm.
Ivanovic shrugged off Suarez and immediately complained to referee Kevin Friend, who didn't see the incident and didn't speak to Suarez.
Suarez apologized in a statement released by Liverpool later Sunday.
"I am deeply sorry for my inexcusable behaviour earlier today during our match against Chelsea," Suarez said in the statement. "I have issued an apology and have tried to contact Branislav Ivanovic to speak to him personally. I apologise also to my manager, playing colleagues and everyone at Liverpool Football Club for letting them down."
Liverpool managing director Ian Ayre called Suarez's action "not befitting of any player wearing a Liverpool shirt."
In November 2010, Suarez was banned for seven matches for biting PSV Eindhoven's Otman Bakkal while playing in the Dutch league, earning him the nickname "Cannibal of Ajax."
Professional Footballers' Association chairman Gordon Taylor was critical of Suarez.
"It is very depressing and embarrassing that it should happen," he told BBC Sport. "If it wasn't for all the controversies he's been involved in he would be a more highly regarded player. Players are role models and are highly rewarded. This sets such a bad example."
Suarez was suspended for eight games in December 2011 for making racist insults to Manchester United defender Patrice Evra during a Premier League match. And in the 2010 World Cup quarterfinal, Suarez's handball in overtime prevented a goal by Ghana's Dominic Adiyiah, earning a red card. Asamoah Gyan hit the crossbar with the ensuing penalty kick, and Uruguay advanced in a shootout.
On Sunday, Suarez also gave away a penalty kick with a needless handball, and Eden Hazard converted to put Chelsea ahead 2-1 in the 57th minute. Suarez's goal in the seventh minute of injury time -- one more that initially signaled -- gave Liverpool the draw. He leads the Premier League with 23 goals and has 30 overall this season.
"I think it would be an injustice to Luis Suarez to talk about [the incident]. He has been the best player in the league this season," Liverpool captain Steven Gerrard said. "I think he is the third-best player in the world behind Lionel Messi and Cristiano Ronaldo."
The late goal denied interim Chelsea manager Rafa Benitez a winning return to the club he led to the Champions League title in 2005 and the final of Europe's top competition in '07.
Chelsea had looked like it was headed for a win with a goal from Oscar and Hazard's penalty either side of substitute Daniel Sturridge's close-range strike.
With Tottenham winning earlier in the day, the draw was a blow to Chelsea's Champions League expectations as it dropped the Blues to fourth, just a point ahead of their London rivals.
Benitez remains a hugely divisive figure and that was highlighted no better than with his stepping back out into Anfield for the first time nearly three years after leaving.
Supporters warmly welcomed the man viewed as a returning hero in these parts -- the only ones not applauding were those from Chelsea whose objections to the Spaniard directly result from his red roots.
Having won a fifth European Cup in 2005, Benitez added the FA Cup a year later before returning to the Champions League final in 2007, and he qualified for Europe's elite club competition every season except for his last -- without doubt the most tumultuous and difficult of his time at the club.
His affinity with Liverpool supporters has only been strengthened by his support for the Hillsborough families and Saturday he visited the memorial at Anfield and laid flowers and a single red rose for Anne Williams. A minute's applause was held for the longtime justice campaigner, whose 15-year-old son Kevin died in the disaster, after she passed away earlier this week just a couple of days after attending the 24th anniversary memorial service.
Information from The Associated Press and Press Association was used in this report.